Question: Michael is 3 times as old as Tiffany. Twelve years ago, Michael was 5 times as old as Tiffany. How old is Michael now?
Explanation: We can use the given information to write down two equations that describe the ages of Michael and Tiffany. Let Michael's current age be $m$ and Tiffany's current age be $t$ The information in the first sentence can be expressed in the following equation: $m = 3t$ Twelve years ago, Michael was $m - 12$ years old, and Tiffany was $t - 12$ years old. The information in the second sentence can be expressed in the following equation: $m - 12 = 5(t - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $m$ , it might be easiest to solve our first equation for $t$ and substitute it into our second equation. Solving our first equation for $t$ , we get: $t = m / 3$ . Substituting this into our second equation, we get: $m - 12 = 5($ $(m / 3)$ $- 12)$ which combines the information about $m$ from both of our original equations. Simplifying the right side of this equation, we get: $m - 12 = \dfrac{5}{3} m - 60$ Solving for $m$ , we get: $\dfrac{2}{3} m = 48$ $m = \dfrac{3}{2} \cdot 48 = 72$.